A particle moves from a point$(-2\hat{i}+5\hat{j})\text{ to }(4\hat{j}+3\hat{k})$  when a force of $(4\hat{i}+3\hat{j})$ N is applied. How much work has been done by the force?

Given    ${\overrightarrow{r}}_1=-2\hat{i}+5\hat{j} \text{and }{\overrightarrow{r}}_2=4\hat{j}+3\hat{k}$

$\Rightarrow \text{displacement }{\overrightarrow{r}}_2-{\overrightarrow{r}}_1=2\hat{i}-\hat{j}+3\hat{k}$

Since force   $\overrightarrow{\mathrm{F}}=4\hat{\mathrm{i}}+3\hat{\mathbf{j}}$
Work done  = $\overrightarrow{\mathrm{F}}\cdot \overrightarrow{\mathrm{r}}=(4\hat{\mathrm{i}}+3\hat{\mathrm{j}})\cdot (2\hat{\mathrm{i}}-\hat{\mathrm{j}}+3\hat{\mathrm{k}})=8-3=5\mathrm{J}$